JP3242950B2 - Predictive control method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a predictive control method for predicting a control amount at the time of sampling a nonlinear control object such as a manipulator.

[0002]

2. Description of the Related Art Conventionally, as a control method of a non-linear controlled object such as a manipulator, a method combining non-linear compensation and feedback control, and an inverse plant method of obtaining an operation amount from a mathematical model of the non-linear controlled object have been considered. In each of these methods, accurate control cannot be performed unless a mathematical model (a mathematical model of dynamic characteristics) is unknown.

[0003] In addition to the method described above, a neural circuit obtains the dynamic characteristics of a control target by learning using the neural circuit, so that a neural circuit that can be controlled even if the mathematical model is unknown. Several control methods of the non-linear control object used have been proposed.

[0004]

However, in each of the former methods, accurate control cannot be performed unless the mathematical model of the controlled object (the mathematical model of dynamic characteristics) is unknown. In addition, since the latter methods are feedforward controls that calculate an operation amount from a target control amount, compensation for disturbance cannot be performed.

SUMMARY OF THE INVENTION The present invention has been made in view of the above circumstances, and it is possible to perform predictive control even for a controlled object whose mathematical model of dynamic characteristics is unknown, and to predict a controlled object capable of compensating for a disturbance. It is an object to provide a control method.

[0006]

The present invention includes the following steps to achieve the above object. That is, the invention corresponding to claim 1 provides a predictive control method for performing predictive control by giving an operation amount to a control target to be controlled, wherein a multilayer neural network is used as an identifier of the control target, and enter the control amount and the operation amount during the sample relative to the control target, where the time of the sampling
A first step of predicting a control amount after a fixed time, a second step of calculating an error between the predicted value obtained in the first step, and a target control amount of the control object, and a second step of obtained in
Enter the control amount error to said identifier, seeking error in the operation amount of the present time by the error back propagation method, by N if a third step of correcting the manipulated variable applied to the controlled object. The invention corresponding to claim 2 includes a fourth step in which the second and third steps in claim 1 are repeatedly performed.

[0007]

According to the present invention, the manipulated variable and the controlled variable of the controlled object are input to the multilayer neural network, and the control variable at the time of sampling can be predicted by forward calculation, and can be predicted by the error back propagation calculation of the neural circuit. The amount of correction of the manipulated variable can be calculated from the difference between the control amount and the target control amount, and this allows the mathematical model of the dynamic characteristics of a controlled object with unknown characteristics or a highly controlled nonlinear dynamic characteristic. Can be controlled even if the control target is unknown (a control target having unknown characteristics or a control target having strong nonlinearity in dynamic characteristics). In the forward calculation of the multilayer neural network, the control amount realized at that time is input together with the operation amount, and the operation amount is corrected so that the control amount after the sampling cycle approaches the target control amount. Can be compensated for.

[0008]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a block diagram showing a schematic configuration of an apparatus for carrying out the present invention. The control target includes, for example, a manipulator 1, an identifier 2 composed of a multilayer neural network model, an operation amount generator 3, an integrator 4, a switch 5, and a time delay element 7 provided in a feedback loop 6.

Here, as an example of the control object, FIG.
The following describes an example of a two-joint manipulator having a first joint 11 and a second joint 12 shown in FIG. 1, but the present invention is not limited to this, and other non-linear control targets may be used. Manipulator 1
Is the angle that the first link 13 makes with the x-axis is the first joint angle θ1,
The angle between the extension of the link 13 and the second link 14 is defined as a second joint angle θ2, and the first joint torque τ1
The second joint torque .tau.2 is applied to the second joint 12 in the positive direction of each joint angle.

At time nΔt, the manipulator 1 receives a joint angle torque Un = (τ1, n, τ2, n) ^T which is an operation amount, where Xn + 1 = F (Xn, Un), that is, State X _{n + 1} which is a control amount after sampling period Δt
_{= (Θ 1, n + 1} , θ 2, n + 1, θ'1, n + 1, θ'2,
_{n + 1} ) ^T is measured.

Here, τ1, n and τ2, n indicate the first joint torque and the second joint torque at time nΔt, respectively. Un indicates a torque vector. θ '
_{1, n} and θ ′ _{2, n} indicate the first joint angular velocity and the second joint angular velocity at time nΔt, and X _n is a state vector having these as components.

The identifier 2 has a multilayer neural network model as shown in FIGS. 3 (a) and 3 (b). The first function of the identifier 2 is as shown in FIG. As shown in (a), the operation amount Un and the control amount Xn of the manipulator 1 are determined.
Is input, the predicted value Zn + 1 of the control amount at the time of sampling (after the sampling period) is output. The second function is as shown in FIG. Is to calculate the error ΔUn of the torque Un by the error back propagation calculation using the difference between the target value dn + 1 and the target value dn + 1. In the neural circuit model of FIG. 3, the right side is the first layer, and the left side is the final layer.

Here, the error back propagation learning method will be described with reference to the flowchart of FIG. This backpropagation learning method is currently the most commonly used method. This method is a method of calculating the steepest descent direction of an error function surface defined in a connection load space and changing the connection load in that direction. First, an initial value of the connection weight w is set by a random number (S1). Next, data that the neural network model wants to learn, that is, input signals Ui, Xi,
Then, a desired output signal ti for the input is set (S2). Here, i = 1, 2,..., Data max.

Next, the amount of change in the connection load is calculated for all the data (S5-S10). Data input signals Ui and Xi are input to a neural circuit model, and output signals (output signals when Xi and Ui are input to the neural circuit model) Z
i is obtained by forward calculation (S6). From the output value Zi and the desired output value ti, an error function Ei is defined as follows (S7). 1/2 (ti-Zi) ^T (Ti-Zi)

Further, the steepest descent direction Δwi of the error function Ei in the connection weight space (the amount of change in the connection weight of the neural circuit calculated from the i-th learning data) is calculated by the error back propagation calculation (S8). In the equation of S8, dE
Both i / dw and dg / dw indicate partial differentiation.
The calculations from S6 to S8 are performed for all data (S
5, S9, S10). Then, using the obtained steepest descent direction of each data, the coupling load w is changed as follows (S11). That is, w + ε (Δw1 + Δw2 +... + Δwdatamax) → w. Here, ε is a parameter of the amount of change in the connection weight called a learning constant. Iterate the steps mentioned above
The error function is reduced by repeating the process (S
3, S4, S12, S13). The predicted value Zn + 1 of the dynamics of the manipulator 1 of the identifier 2 having completed learning as described above can be expressed as a function as follows. That is, Zn + 1 = g (Xn, Un, W ^* ). In this case, W ^* indicates the connection weight of the neural network model after learning, and Zn + 1 is the predicted value of the control amount at time (n + 1) Δt. In FIG. 1, an operation amount generator 3 has a function of generating an initial operation amount Uo only at the start of exercise.

The correction amount ΔUn from the identifier 2 is added to the operation amount Un by the integrator 4. The control amount prediction and the correction of the manipulated variable after the sampling period are performed once or a plurality of times within the sampling time. The switch 5 operates every sampling time (unit time), and has a function of outputting the operation amount Un to the manipulator 1 at this time.

Next, a control operation of the manipulator 1 will be described with reference to FIG. First, a target trajectory (dn) is set (S20). Then, the operation amount U0 = U (d0) for the manipulator 1 to take the initial posture (X0 = d0).
) Is set by the manipulated variable generator 3 (S 21), and this is set via the integrator 4 and the switch 5.
To the initial position of the target trajectory of the manipulator 1. When the movement of the manipulator 1 is started, the prediction of the control amount after the sampling time Δt and the correction of the operation amount by the error back propagation method are repeated (S25-S).
31).

The manipulated variable Un and the control variable Xn fed back via the time delay 7 are input to the neural circuit model,
The predicted value Zn + 1 of the control amount after the sampling time Δt seconds is obtained (S26). The predicted value Zn + 1 and the target value dn + 1
The error function En + 1 is defined as follows from the difference ΔXn + 1 = target value dn + 1−predicted value Zn + 1 (S27). En + 1 = 1/2 (ΔXn + 1) ^T Ks (ΔXn + 1) where Ks is a gain matrix. The correction amount of the input signal is obtained by the above-described error back propagation method so as to reduce the error function (S28). ΔUn = − (dEn + 1) / (dUn) = dg (Xn, Un, W ^* ) / dUn × (KsΔXn + 1) ΔXn = − (dEn + 1) / (dXn) = dg (Xn, Un, W) ^* ) / DXn × (KsΔXn + 1) The value of the manipulated variable in the input signal is (Un + ΔUn)
→ Un) (S29).

Again, the predicted value Zn + 1 of the control amount after the sampling time, which is the corrected input signal, is obtained, and the correction of the manipulated variable is repeated. After the correction is repeated a fixed number of times (k), the manipulated variable is input to the manipulator 1 at the sampling time (S32). Repeat the above steps for the final time (time
f) (S22, S23, S33, S3)
5).

At the initial time, the manipulated variable Un from the manipulated variable generator 3 is given. Thereafter, the value of the manipulated variable Un-1 at the previous time is set to the initial value of the manipulated variable Un at the current time ( S
34). If the neural network model has sufficiently learned the dynamics of the manipulator, the connection weight of the neural network model is a correct value. Therefore, if an error occurs between the predicted value Zn + 1 and the target value dn + 1, it means that the input signal Control amount Xn
And the operation amount Un. Since the control amount Xn is a measured value, the control amount Xn is corrected by the operation amount Un so as to approach the target value dn + 1 after the sampling time from the current control amount Xn. If the sampling time is short and the manipulated variable at one time is close to the manipulated variable at the next time, the value of the manipulated variable that reaches the target state in a small number of times by using the value of the manipulated variable at the previous time as the initial value Can be expected.

FIGS. 6 and 7 show simulation results when the manipulator of FIG. 2 is to be controlled and the repetition performed at the sampling time is three times in the flowchart of FIG. 5, and FIG. FIG. 6B shows the first joint angle, FIG. 6B shows the second joint angle, FIG. 7A shows the waveform diagram of the first joint torque, and FIG. 7B shows the waveform diagram of the second joint torque. The horizontal axis in FIGS. 6 and 7 indicates the exercise time (2
The vertical axis in FIG. 6 is the joint angle trajectory, the unit is radian (rad), and the vertical axis in FIG. 7 is the torque waveform, and the unit is Newton meter (Nm). Further, the broken line in FIG. 6 indicates the target trajectory, and the solid line indicates the realized trajectory. As is apparent from FIG. 6, since the realized trajectory (solid line) almost overlaps the target trajectory (dashed line),
It can be seen that the vehicle follows the target trajectory well. The torque waveform in this case is as shown in FIG. 7. In the flowchart of FIG. 5, in an experiment in which the number of repetitions performed at the sampling time is four or more, the realized trajectory is closer to the target trajectory, and the torque waveform is further smooth. Became.

It should be noted that the present invention is not limited to the above-described embodiment, but may be variously modified without departing from the gist of the present invention. For example, in the above-described embodiment, a manipulator has been described as an example of a non-linear control target, but other linear control targets can be similarly applied.

In the above embodiment, the simplest example is 1
Although the example in which only the control amount after the sampling time is predicted has been described, when the order of the differential equation indicating the dynamic characteristic of the control target is higher than the first order, the control amount is predicted at a time further than one sampling time. It is necessary to correct the manipulated variable by the back propagation method from the error of the predicted value. Even in such a case, by learning not only the control amount prediction after one sampling time but also the neural circuit model so as to predict the previous control amount such as after two sampling times and three sampling times. In addition, it is possible to control even a controlled object having a high order of a differential equation showing dynamic characteristics.
8 and 9 show neural circuit models for predicting the control amount up to two sampling times later.

FIG. 8 shows a neural network model composed of three layers. The operation amount Un and the control amount X from the first layer (rightmost layer) in FIG.
When n is input, a predicted value Zn + 1 of the control amount after one sampling time and a predicted value Zn + 2 of the control amount after two sampling times are output from the third layer. In the error backpropagation calculation in FIG. 8B, the error ΔXn + 1 = d of the predicted value after the sampling time
Error Δ between n + 1−Zn + 1 and the predicted value after two sampling times
Xn + 2 = dn + 2−Zn + 2 is back-propagated from the third layer, and the correction amount ΔUn of the manipulated variable is obtained.

FIG. 9 shows a neural network model composed of five layers. The operation amount Un and the control amount X are calculated from the first layer (rightmost layer) in FIG.
When n is input, a predicted value Zn + 1 of the control amount after one sampling time from the third layer and a predicted value Zn + 2 of the control amount after two sampling times from the fifth layer are output. And FIG.
In the error backpropagation calculation of (b), the error ΔXn + 1 = dn + 1−Zn + 1 of the predicted value after one sampling time is obtained from the third layer.
Error ΔXn + 2 = dn + 2 of the predicted value after two sampling times
−Zn + 2 is back-propagated from the fifth layer, and the correction amount ΔU
n is required.

[0026]

According to the present invention described above, there is provided a predictive control method for a controlled object which can control a controlled object whose mathematical model of dynamic characteristics is unknown and can also compensate for a disturbance. be able to.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a schematic configuration of an apparatus for implementing the method of the present invention.

FIG. 2 is a view for explaining the manipulator of FIG. 1;

FIG. 3 is a flowchart for explaining a first example of the identifier in FIG. 1;

FIG. 4 is a diagram for explaining a learning method in an initial state of FIG. 1;

FIG. 5 is a flowchart for explaining the control operation of FIG. 1;

FIG. 6 is a diagram for explaining the operation and effect of the embodiment of FIG. 1;

FIG. 7 is a view for explaining the operation and effect of the embodiment of FIG. 1;

FIG. 8 is a view for explaining a second example of the identifier in FIG. 1;

FIG. 9 is a view for explaining a third example of the identifier in FIG. 1;

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Manipulator, 2 ... Identifier, 3 ... Manipulated variable generator,
4 integrator, 5 switch, 6 feedback loop, 7 delay element.

Claims (3)

(57) [Claims] 1. A predictive control method for performing predictive control by giving an operation amount to a control target to be controlled, wherein a multi-layer neural circuit is used as an identifier of the control target, and the identifier uses the neural network for sampling the control target. A first step of inputting a control amount and an operation amount of the control target and predicting a control amount after a predetermined time from the sampling time; a prediction value obtained in the first step; and a target control amount of the control target. A second step of obtaining an error; and inputting the control amount error obtained in the second step to the identifier, and operating the target control amount by an error back propagation method.
Of the target control amount,
A third step of multiplying the sensitivity to obtain a correction amount of the manipulated variable . 2. A correction amount of the operation amount for one time,
Determination through repetition of the first to third steps
The predictive control method according to claim 1, wherein: 3. The predictive control method according to claim 1, wherein the first step predicts the control amount after an integer multiple of the sampling period from the time of the sampling or in units other than the sampling period.